The Experts below are selected from a list of 38019 Experts worldwide ranked by ideXlab platform
Stefano Pigola - One of the best experts on this subject based on the ideXlab platform.
-
the calderon zygmund inequality and sobolev spaces on noncompact Riemannian Manifolds
Advances in Mathematics, 2015Co-Authors: Batu Guneysu, Stefano PigolaAbstract:Abstract We introduce the concept of Calderon–Zygmund inequalities on Riemannian Manifolds. For 1 p ∞ , these are inequalities of the form ‖ Hess ( u ) ‖ L p ≤ C 1 ‖ u ‖ L p + C 2 ‖ Δ u ‖ L p , valid a priori for all smooth functions u with compact support, and constants C 1 ≥ 0 , C 2 > 0 . Such an inequality can hold or fail, depending on the underlying Riemannian geometry. After establishing some generally valid facts and consequences of the Calderon–Zygmund inequality (like new denseness results for second order L p -Sobolev spaces and gradient estimates), we establish sufficient geometric criteria for the validity of these inequalities on possibly noncompact Riemannian Manifolds. These results in particular apply to many noncompact hypersurfaces of constant mean curvature.
Yu. G. Nikonorov - One of the best experts on this subject based on the ideXlab platform.
-
KILLING VECTOR FIELDS OF CONSTANT LENGTH ON LOCALLY SYMMETRIC Riemannian Manifolds
Transformation Groups, 2008Co-Authors: V. N. Berestovskiĭ, Yu. G. NikonorovAbstract:In this paper nontrivial Killing vector fields of constant length and the corresponding ows on smooth complete Riemannian Manifolds are investigated. It is proved that such a ow on symmetric space is free or induced by a free isometric action of the circle S1. Examples of unit Killing vector fields generated by almost free but not free actions of S1 on locally symmetric Riemannian spaces are found; among them are homogeneous (nonsimply connected) Riemannian Manifolds of constant positive sectional curvature and locally Euclidean spaces. Some unsolved questions are formulated.
-
Killing vector fields of constant length on Riemannian Manifolds
Siberian Mathematical Journal, 2008Co-Authors: V. N. Berestovskii, Yu. G. NikonorovAbstract:We study the nontrivial Killing vector fields of constant length and the corresponding flows on complete smooth Riemannian Manifolds. Various examples are constructed of the Killing vector fields of constant length generated by the isometric effective almost free but not free actions of S 1 on the Riemannian Manifolds close in some sense to symmetric spaces. The latter Manifolds include “almost round” odd-dimensional spheres and unit vector bundles over Riemannian Manifolds. We obtain some curvature constraints on the Riemannian Manifolds admitting nontrivial Killing fields of constant length.
-
Killing vector fields of constant length on Riemannian Manifolds
arXiv: Differential Geometry, 2006Co-Authors: V. N. Berestovskii, Yu. G. NikonorovAbstract:In this paper nontrivial Killing vector fields of constant length and corresponding flows on smooth complete Riemannian Manifolds are investigated. It is proved that such a flow on symmetric space is free or induced by a free isometric action of the circle $S^1$. The properties of the set of all points with finite (infinite) period for general isometric flow on Riemannian Manifolds are described. It is shown that this flow is generated by an effective almost free isometric action of the group $S^1$ if there are no points of infinite or zero period. In the last case the set of periods is at most countable and naturally generates an invariant stratification with closed totally geodesic strata; the union of all regular orbits is open connected everywhere dense subset of complete measure. Examples of unit Killing vector fields generated by almost free but not free actions of $S^1$ on Riemannian Manifolds close in some sense to symmetric spaces are constructed; among them are "almost round" odd-dimensional spheres, homogeneous (non simply connected) Riemannian Manifolds of constant positive sectional curvature, locally Euclidean spaces, and unit vector bundles over Riemannian Manifolds. Some curvature restrictions on Riemannian Manifolds admitting nontrivial Killing vector fields of constant length are obtained. Some unsolved questions are formulated.
S K Yadav - One of the best experts on this subject based on the ideXlab platform.
-
projective curvature tensor of Riemannian Manifolds admitting a projective semi symmetric connection
Universal Journal of Mathematics and Applications, 2020Co-Authors: S K Chaubey, Pankaj R B Kanaujia, S K YadavAbstract:The aim of the present paper is to study the properties of Riemannian Manifolds equipped with a projective semi-symmetric connection.
-
Riemannian Manifolds admitting a projective semi symmetric connection
arXiv e-prints, 2017Co-Authors: S K Chaubey, S K YadavAbstract:The aim of the present paper is to study the properties of Riemannian Manifolds equipped with a projective semi-symmetric connection.
Fengyu Wang - One of the best experts on this subject based on the ideXlab platform.
-
analysis for diffusion processes on Riemannian Manifolds
2013Co-Authors: Fengyu WangAbstract:Diffusion Processes on Riemannian Manifolds Reflecting Diffusion Processes on Riemannian Manifolds with Boundary Coupling and Applications Harnack Inequalities and Applications Functional Inequalities and Applications Formulae for the Curvature and Second Fundamental Form Equivalent Semigroup Inequalities for the Lower Bounds of Curvature and Second Fundamental Form Modified Curvature and Applications Robin Semigroup and Applications Stochastic Analysis on the Path Space Over Manifolds with Boundary Subelliptic Diffusion Processes.
-
gradient estimates and harnack inequalities on non compact Riemannian Manifolds
Stochastic Processes and their Applications, 2009Co-Authors: Marc Arnaudon, Fengyu Wang, Anton ThalmaierAbstract:A gradient-entropy inequality is established for elliptic diffusion semigroups on arbitrary complete Riemannian Manifolds. As applications, a global Harnack inequality with power and a heat kernel estimate are derived.
Li Siran - One of the best experts on this subject based on the ideXlab platform.
-
Weak Continuity of the Cartan Structural System and Compensated Compactness on Semi-Riemannian Manifolds with Lower Regularity
2021Co-Authors: Chen, Gui-qiang G., Li SiranAbstract:We are concerned with the global weak continuity of the Cartan structural system -- or equivalently, the Gauss--Codazzi--Ricci system -- on semi-Riemannian Manifolds with lower regularity. For this purpose, we first formulate and prove a geometric compensated compactness theorem on vector bundles over semi-Riemannian Manifolds with lower regularity (Theorem 3.2), extending the classical quadratic theorem of compensated compactness. We then deduce the $L^p$ weak continuity of the Cartan structural system for $p>2$: For a family $\{\mathcal{W}_\varepsilon\}$ of connection $1$-forms on a semi-Riemannian manifold $(M,g)$, if $\{\mathcal{W}_\varepsilon\}$ is uniformly bounded in $L^p$ and satisfies the Cartan structural system, then any weak $L^p$ limit of $\{\mathcal{W}_\varepsilon\}$ is also a solution of the Cartan structural system. Moreover, it is proved that isometric immersions of semi-Riemannian Manifolds into semi-Euclidean spaces can be constructed from the weak solutions of the Cartan structural system or the Gauss--Codazzi--Ricci system (Theorem 5.1), which leads to the $L^p$ weak continuity of the Gauss--Codazzi--Ricci system on semi-Riemannian Manifolds. As further applications, the weak continuity of Einstein's constraint equations, general immersed hypersurfaces, and the quasilinear wave equations is also established.Comment: 64 page
-
Weak Continuity of the Cartan Structural System and Compensated Compactness on Semi-Riemannian Manifolds with Lower Regularity
2020Co-Authors: Chen, Gui-qiang G., Li SiranAbstract:We are concerned with the global weak continuity of the Cartan structural system $-$ or equivalently, the Gauss-Codazzi-Ricci system $-$ on semi-Riemannian Manifolds with lower regularity. For this purpose, we first formulate and prove a geometric compensated compactness theorem on vector bundles over semi-Riemannian Manifolds with lower regularity (Theorem 3.4), extending the classical quadratic theorem of compensated compactness. We then deduce the $L^p$ weak continuity of the Cartan structural system for $p>2$: For a family $\{\mathcal{W}^\varepsilon\}$ of connection $1$-forms on a semi-Riemannian manifold $(M,g)$, if $\{\mathcal{W}^\varepsilon\}$ is uniformly bounded in $L^p$ and satisfies the Cartan structural system, then any weak $L^p$ limit of $\{\mathcal{W}^\varepsilon\}$ is also a solution of the Cartan structural system. Moreover, it is proved that isometric immersions of semi-Riemannian Manifolds into semi-Euclidean spaces can be constructed from the weak solutions of the Cartan structural system or the Gauss-Codazzi-Ricci system (Theorem 5.1), which leads to the $L^p$ weak continuity of the the Gauss-Codazzi-Ricci system on semi-Riemannian Manifolds. As further applications, the weak continuity of Einstein's constraint equations, general immersed hypersurfaces, and the quasilinear wave equations is also established.Comment: 45 page
-
Global Weak Rigidity of the Gauss-Codazzi-Ricci Equations and Isometric Immersions of Riemannian Manifolds with Lower Regularity
'Springer Science and Business Media LLC', 2017Co-Authors: Chen, Gui-qiang G., Li SiranAbstract:We are concerned with the global weak rigidity of the Gauss-Codazzi-Ricci (GCR) equations on Riemannian Manifolds and the corresponding isometric immersions of Riemannian Manifolds into the Euclidean spaces. We develop a unified intrinsic approach to establish the global weak rigidity of both the GCR equations and isometric immersions of the Riemannian Manifolds, independent of the local coordinates, and provide further insights of the previous local results and arguments. The critical case has also been analyzed. To achieve this, we first reformulate the GCR equations with div-curl structure intrinsically on Riemannian Manifolds and develop a global, intrinsic version of the div-curl lemma and other nonlinear techniques to tackle the global weak rigidity on Manifolds. In particular, a general functional-analytic compensated compactness theorem on Banach spaces has been established, which includes the intrinsic div-curl lemma on Riemannian Manifolds as a special case. The equivalence of global isometric immersions, the Cartan formalism, and the GCR equations on the Riemannian Manifolds with lower regularity is established. We also prove a new weak rigidity result along the way, pertaining to the Cartan formalism, for Riemannian Manifolds with lower regularity, and extend the weak rigidity results for Riemannian Manifolds with unfixed metrics.Comment: 42 pages, Journal of Geometric Analysis, 201
